The modeling of dynamic systems is an important step in the development of computer based interpretation of dynamic systems. Attempts have been made to model such diverse systems as financial markets, chemical plant operations and aircraft operations. However, typical statistical and numerical interpretation methods have failed because the parameters used to model systems often lead to faulty interpretation of the state that the system is in. This is because there are not always precise boundaries between system parameters and system states.
To help alleviate this problem, the concept of fuzzy sets was developed. The purpose of fuzzy sets is to deal with classes that have no sharply defined criteria of class membership. This helps to deal with the uncertainty that exists in complex dynamic systems.
Fuzzy systems are useful to help encode human knowledge into dynamic systems by allowing for the presence of uncertainty. Fuzzy systems consist of three parts, a fuzzifier, a rule and a defuzzifier. Inputs in the form of numerical data measured in the dynamic system are inputted into the fuzzifier. The fuzzifier prepares the exact numerical data for analysis in the rule base. The numerical data is mapped into fuzzy sets within a certain degree of certainty.
The fuzzy rule base encodes expert knowledge into sets of if/then rules. The number of rules depends on the complexity of the system, which is based on the number of inputs and the number of sets defined on each input domain. The defuzzifier converts the fuzzy output of the fuzzy rule base into exact numerical values if needed.
The drawback to this approach is that as the number of inputs increase, the size of the rule base grows exponentially. Thus, current fuzzy systems are inappropriate for complex dynamic systems. What is needed is an efficient way to apply fuzzy systems to interpret complex dynamic systems.